Question #9eb92

1 Answer
Sep 27, 2017

Use the Power Rule and Chain Rule to write h'(x)=4/5 (f(x))^{-1/5} * f'(x)=(4f'(x))/(5 root(5){f(x)}).

Explanation:

The Power Rule says that d/(dx) (x^{n})=nx^{n-1} for any number n. The Chain Rule says that d/(dx)(g(f(x)))=g'(f(x)) * f'(x) when f is differentiable at the value x and g is differentiable at the value f(x).

For the problem at hand, g(x)=root(5){x^{4}}=x^{4/5} and therefore g'(x)=4/5 x^{-1/5}=4/(5 root(5){x}).

Therefore h'(x)=d/(dx)(g(f(x)))=4/5 (f(x))^{-1/5} * f'(x)=(4f'(x))/(5 root(5){f(x)})